Modeling short sea wave energy distributions in the far wakes of ships

Abstract

A mathematical model based on the spectral energy balance equation for suppression of shortwave energy in centerline ship wakes is developed. At distances behind a ship of more than a few ship lengths, the dominant influences on short wave energy are the growing effects of wind and nonlinear energy transfer from longer waves, and the attenuating effects of turbulence and viscous attenuation which can be greatly enhanced by surface film distributions which are modified by passage of the ship. These influences are modeled as "source terms" in the energy balance equation. The model is exercised using turbulence data from scale model experiments and surface film distributions measured in an actual ship wake. Agreement between the resulting distribution of Bragg-scattering wave energy and radar image intensity in the far wake is excellent. The influences of variations in the source term model parameters are explored numerically. 96(C6):High-resolution measurements of surface-active film redistribution in ship wakes, J. Geoph•s. Res., 97(C-4):5231-5252, 1992. Phillips O., The scattering of gravity waves by turbulence, Journal of Fluid Mechanics, 5(12):177-192, 1958. Plant W.J., A relationship between wind stress and wave slope, J. Geoph.•ls. Res., 87:1961-1967, 1982. Skop R.A., O.M. Griffin, K.R. Nicolas, and T.F. Swean, Jr., Modification of wave spectra by currents in the wake of a surface ship, Nrl memorandum report 6336, U.S. Naval Research Laboratory,

SHIP WAKES AND THEIR RADAR IMAGES

“…To integrate the energy balance (Equation 20), mathematical models for the source terms are necessary. The approach taken by Milgram et al (1993b) was to develop a model to be used outside the wake and to add corrective terms to this model inside the wake. The model outside the wake is equivalent to the ones used by Lyzenga & Bennett (1988) and Lyzenga (1991).…”

“…They used knowledge about the damping of specific wave lengths by surfactants and made inferences from the effects on other wavelengths. This analysis is summarized by Milgram et al (1993b), who also examined the sensitivity of results to its magnitude. The effect is small, and for subsequent examples here, this source term, S wnl , is set to zero.…”

Measurement of turbulence in the oceanic mixed layer using Synthetic Aperture Radar (SAR)

“…The interaction of turbulence and waves may be considered weak if the energy gained by the turbulence through interaction with waves is small when compared with the energy transfer due to internal turbulence interactions. Hence, the accuracy of the simulation may be improved by including in the wave action conservation calculation the effects of exchange of energy between the turbulence and the wave system: some authors have operated models which directly represent turbulent energy dissipation (spectral modification caused by turbulent fluctuations within the wake), such as Milgram et al (1993) and True et al (1993). In the discussion presented in this paper, the effects of turbulent dissipation of short-wave energy have not been accounted for in the calculation of the modulated wave spectrum.…”

“…A schematic of a typical ship wake is presented in Fig. 1, and examples of turbulent wake features in operational SAR images can be found extensively in the literature (Munk et al, 1987;Lyden et al, 1988;Milgram et al, 1993;Hennings et al, 1999;Toporkov et al, 2011). Simulation of ship-wake turbulence and the NRCS response has previously been studied by, for example, Reed et al (1990), True et al (1993) and Fujimura et al (2011).…”

Study of Electromagnetic Scattering From Ship Wakes on Pec Sea Surfaces by the Small-Slope Approximation Theory

“…The wave height distribution of Kelvin wakes has already had certain expressions beneficial to the study of all kinds of ships' sizes and velocities. However, the turbulent wakes [24] refer to the volume scattering of foam layers. So this paper only studies Kelvin wakes of ships.…”